Study Of Lump Solutions And Interaction Solutions For Several High Dimensional Nonlinear Evolution Equations

Based on the bilinear method,the paper discuss lump solutions,interaction solutions and breather wave solutions to several types of high-dimensional nonlinear evolution equations by symbolic calculation.Using figure,we analyze their geometrical,physical and dynamic characteristics.The details are as follows:The first chapter,this chapter focuses on the bilinear method,the development and research of lump solution,interaction solution and breather wave solution,and the theorem of lump solution,and introduce the main work of this paper.The second chapter,based on the method given by Professor Ma Wenxiu,we obtained three NLEEs of lump solutions and interaction solutions by symbolic calculation.(1)The lump solution and the interaction solution of the generalized fifth-order KdV equation are studied.The Lump solution is obtained by the positive quadratic function solution transformation.The interaction solution includes the interaction between lump and the hyperbolic cosine function and the interaction between lump and the exponential function.(2)The lump solution of a(2+1)-dimensional bSK equation is studied.(3)The lump solution and the interaction solution between lump and exponential function of the generalized Kadomtsev-Petviashvili equation are studied.And we further studied the physical trajectory of the interaction solution by figure.In the third chapter,we obtained two NLEEs of lump solutions and interaction solutions by using symbolic calculation.(1)The lump solution and the interaction solution between the lump and exponential functions to the Potential KadomstevPetviashvili equation are studied,and according to the obtained figure,we analyzed the nature of the interaction solution.(2)The lump solution and the abundant interaction solution to the BKP-Boussinesq equation are calculated.The interaction solution includes the interaction among the exponential function,the sine function and the cosine function,the periodic solitary wave solution,the interaction among exponential and tangent functions and hyperbolic tangent functions.And we further analyze the initial velocity of lump in the x and y directions.In the fourth chapter,based on Hirota bilinear method and generalized bilinear method,the lump solution,interaction solution and breather wave solution of KPBBM equation and KPB-like equation are studied,respectively.(1)Using the Hirota bilinear method,we studied the lump solution,interaction solution and breather wave solution to the KP-BBM equation.we give the general formula of the lump solution original coordinates and the initial velocity of lump in the x and y directions.(2)Using the generalized bilinear method,we obtained lump solution,interaction solution of the arbitrary function and breather wave solution to the KPB-like equation.In the lump solution,some special coordinates are obtained by taking the parameters,and we further analyze of the physical meaning of the lump solution.Finally,the research work of this paper is summarized,and the related research in the next step is prospected.